Postfix error when trying to send message to web

I am getting an error when I try to send an email from the inside network (where my server is too) to the internet, (local to local goes perfect), this is the error i get:

This is the mail system at host xxx

I'm sorry to have to inform you that your message could not
be delivered to one or more recipients. It's attached below.

For further assistance, please send mail to <postmaster>

If you do so, please include this problem report. You can
delete your own text from the attached returned message.

The mail system

<xxx@xxx>: Host or domain name not found. Name service error for
name=xxx type=A: Host found but no data record of requested type.

Also when I send a mail from the internet to my server nothing is being received, but there is no postmaster message coming back that the smtp server (not the local one, the one on the web) isn't being delivered...

<xxx@xxx>: Host or domain name not found. Name service error for
name=xxx type=A: Host found but no data record of requested type.

Click to expand...

This is saying you need some DNS records for your domain and your mail server. Your mail server needs matching forward and reverse DNS records, and it should announce itself as whatever you set the forward name as. If you are using NAT, this will be related to whatever the IP address is on your Internet connection.

Your domain (in this case, whatever comes after the @) needs at least either an A or MX record so that the receiving server can check the authenticity of your domain.

Also when I send a mail from the internet to my server nothing is being received,

Click to expand...

Do some testing to and from your server with telnet. An example from your server might be as follows. You should substitute your own info. Remote server responses are italicised. Swap the obvious bits around for testing into your server. This lets you emulate what a mail server does, and might give you some clues as to where it fails (like, are your ports really open, etc).

Your domain (in this case, whatever comes after the @) needs at least either an A or MX record so that the receiving server can check the authenticity of your domain.

Click to expand...

I am sure my server got 1 A and 1 MX record, but my domainhost is having some problems at the moment, maybe that's the problem, I will try this again in about 1-2 days when the server of my domain is fully online again.

Do some testing to and from your server with telnet. An example from your server might be as follows. You should substitute your own info. Remote server responses are italicised. Swap the obvious bits around for testing into your server. This lets you emulate what a mail server does, and might give you some clues as to where it fails (like, are your ports really open, etc).